Question

You deposit $10,00 into an investment account that results in your money earning 5.2% interest compounded monthly. a)How many years will it take for you to have 100,000$ in the account? Answer to the nearest 100th of a year. B) what interest rate would be required to have $100,000 in the account? Answer to the nearest 100th of a year. Changes:you deposit $10,000^ i made a mistake in thew questionB.what interest rate would be required to have $100,000 in the account after 25 years? Answer to the nearest 100th of a year.

Answer 1

Given:

`P=\text{ \$10,000 ; }r=0.052`

a)

A= $100,000

`A=P(1+(r)/(12))^(12t)`
`\begin{gathered} 100000=10000(1+(0.052)/(12))^(12t) \\ (100000)/(10000)=((12.052)/(12))^(12t) \\ 10=(1.0043)^(12t) \\ 10=(1.0533)^t \\ t=44.38 \end{gathered}`

It takes 44.38 years to have $100,000 in the account.

b)

A=$100,000 ; t=25

`\begin{gathered} 100000=10000(1+(r)/(12))^(12(25)) \\ 10=((12+r)/(12))^(300) \\ r=0.0925 \end{gathered}`

Interest rate is 9.25% per year.